I googled a bit and mainly found the SUSE announcement of a security
update to PackageKit (http://www.net-security.org/advisory.php?id=9891),
which is what I think is what should be installed here. I have been
choosing 'do not install', expecting the issue to be related to
repository syncing. But some time has now passed, so I think the issue
is something else.

Oddly, I saw a similar complaint for Fedora, but the various fixes
suggested there involved removing packages that do not have installed.
And using those suggestions is like taking a friends extra medication
because you have similar complaints and do not want to go to the doctor.

Anyone else seen this? Better yet: anyone know the cure?

Where did you get PackageKit-0.4.5-2.31.i586 from? It seems to be
from FACTORY, while libpackagekit-glib10-0.3.11-1.14.1.i586 is from
11.1. (FACTORY would have libpackagekit-glib11 )